Tonality and the Origin of the Major Scale

Tonality is the set of laws that govern how scales are built. In a narrower sense, tonality or key means the set of notes that make up a diatonic scale.

A key and a scale contain the same set of notes. But in the scale, the notes follow one another by step, while in the key, the same notes can come in any order, by step or by leap.

The layout of the scale is no accident

In the major scale, the eight notes are laid out like this: two whole steps, a half step, three whole steps, a half step. For Danhauser, this arrangement comes from the natural resonance of vibrating bodies.

The vibrating body and its harmonics

A vibrating body, such as a string or a pipe, produces a main sound, the generating tone, also called the fundamental, which will be the first note of the scale. Along with it come other, fainter sounds, the harmonics, or overtones. Besides the octave, the two that are easiest to hear are the twelfth and the seventeenth above the generating tone.

Reduced to simple intervals, the 12th and the 17th become the perfect fifth and the major third above the generating tone. These three notes heard together form the major triad: C-E-G. Danhauser's French term for it is “accord parfait majeur”, literally “perfect major chord.”

The three generating chords

The C-E-G chord alone is not enough to form the scale. It needs other chords that meet three conditions:

1. They are, like it, produced by the resonance of a vibrating body, which means they are major triads.
2. They contain a note already present in the first chord, which ties them to it.
3. They contain no note in a chromatic relationship with a note of the first chord, because a diatonic scale cannot contain two notes a chromatic half step apart, such as G and G#.

Only two chords meet all three conditions. If you take G, the fifth above C, as a new generating tone, you get G-B-D. If you make C the fifth of a new generating tone, F, you get F-A-C.

Writing out the notes of these three chords by step, starting on C, gives the diatonic scale of C major. The notes that make up a diatonic scale are called diatonic notes.

The tonal notes

The scale is generated by three generating tones: C, F and G. For this reason Danhauser calls them the tonal notes. They occupy the 1st, 4th and 5th degrees of the scale. Their three triads, I, IV and V, are what English-language textbooks call the primary triads.

Natural scale and tempered scale

The scale that resonance generates, the natural scale in just intonation, is not exactly the scale of the piano. The piano is tuned so that all whole steps are equal and every half step is exactly half a whole step: the octave contains 12 equal half steps. This is equal temperament.

In the natural scale, the perfect fifth is slightly larger than the tempered fifth, and the major third noticeably smaller than the tempered third. As a result, the natural scale contains unequal whole steps, and diatonic half steps that are larger than half a whole step.

The comma

Let's try an experiment. Start on C and go up by pure perfect fifths: G, D, A, E. This E, reached by four fifths, is noticeably higher than the E that the same C produces as its 17th harmonic. The difference is called a comma. It is roughly one ninth of a whole step.

By making the twelve half steps of the octave equal, temperament has a single key play two sounds that would otherwise be slightly different: it treats C# and Db, or B# and C, as the same note, and so makes enharmonic equivalence easy.

You now know where each note of the scale comes from. Next, let's give each degree of the scale its own name.